Best way - TIG with 308 (or 309 or 316) filler wire and back purge
Next best - GMAW with tri-mix and stainless 308 wire (or 309 or 316)
Next next best - GMAW with stainless 308 wire (or 309 or 316) and C25, single pass weld only and you shouldn't get too much carbon pick-up from the shielding gas.
Not really an option unless you are an SMAW god at welding thin wall tube - 3/32" 308/308L-16 or -17 rod at the lowest amps it will run (40-50 amps usually), or 1/16" similar rod at 30-40 amps.
No FCAW, even if you wanted to get a $$$ spool of stainless FCAW-S wire.
Plain ER70 carbon steel wire and C25 will weld the stainless, at least initially, but it WILL rust. Rather quickly, especially due to hot exhaust and road salt and dissimilar metals.
A 2 pound spool of stainless wire (name brand stuff) is probably going to run you about $35 all by itself. No-name or 'off' brand might be about $20. That's US dollars, so in Canadian that's probably about $500CAN

.
3/32" stainless stick is about $10/lb, but you usually have to buy an 8-10 pound can, 1/16" stick is about $14/lb, and again you usually have to buy an 8-10 lb can.